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Explicit Families of Elliptic Curves with Prescribed Mod N Representations

In: Modular Forms and Fermat’s Last Theorem

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  • Alice Silverberg

Abstract

In Part 1 we explain how to construct families of elliptic curves with the same mod 3, 4, or 5 representation as that of a given elliptic curve over Q. In §4 we give equations for the families in the mod 4 case. The mod 3 and mod 5 cases were given in [9] (see also [8]). The results remain true (with the same proofs) with the field of rational numbers replaced by any field whose characteristic does not divide the level.

Suggested Citation

  • Alice Silverberg, 1997. "Explicit Families of Elliptic Curves with Prescribed Mod N Representations," Springer Books, in: Gary Cornell & Joseph H. Silverman & Glenn Stevens (ed.), Modular Forms and Fermat’s Last Theorem, pages 447-461, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1974-3_15
    DOI: 10.1007/978-1-4612-1974-3_15
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